Deciphering genotype‐by‐environment interaction in new soybean lines based on multiple traits using different adaptability and stability methods

Abstract The multi‐environmental trials aid breeders in selecting the best genotypes for specific or general adaptability to different environments before commercial release. This study aimed to assess the stability of 13 new soybean pure lines, along with two controls, in terms of seed yield and important agronomic traits. The assessment was based on a completely randomized block design with three replications across four areas during 2020–2022. Various adaptability methods, including parametric, AMMI, GGE biplot, PCA, and SIIG were employed. The mixed analysis showed that the effects of environment, genotype, and genotype–environment (GE) interaction were significant for most studied traits. The AMMI showed the highest portion of environment (65.89%) in soybean seed yield. Based on all stability parameters, lines 2 and 5 were selected for their average seed yields of 3349 and 3142 kg ha−1, respectively. Additionally, lines 6 and 5 showed the most stability, yielding higher than the average, which were 2992 and 3142 kg ha−1, respectively, according to GGE biplot results. Furthermore, lines 2, 5, and 8 were identified as the ideal genotypes concerning seed yield and other agronomic traits, with high SIIG parameters and yields exceeding the average. Finally, the soybean line 5 was deemed the most suitable due to its higher yield, stability, and early maturity (128‐day growth period). Therefore, line 5 is considered appropriate for its high stability and earliness in various regions of Iran.

hectares and producing approximately 200,000 tons of soybeans, as reported by FAOSTAT statistics (2021).Commercial soybean cultivars in Iran, developed from previous breeding programs, are grown in various regions.Despite the considerable availability of Iranian soybean germplasm, the limited diversity of these varieties does not meet the country's high demand for oil and protein content in human and livestock food rations (Baghbani-Arani et al., 2021).Consequently, industries related to oil and livestock/poultry production rely heavily on imports of soybean seed and soybean meal.This underscores the urgent need to increase soybean yield and production in Iran.
In recent decades, research has focused on breeding programs to develop new lines/genotypes with higher seed/oil yields, as the right agronomic cultivar is a key factor in successful agriculture.It is vital to produce and use cultivars compatible with changing environmental conditions to achieve optimal yields.The variation of agronomic cultivars in different environmental conditions is, therefore, of great importance.Although researchers have introduced seven new soybean cultivars for different areas in Iran, the existing soybean genotypes lack sufficient genetic variation, limiting farmers' ability to choose the right cultivar for every situation (Nehbandani et al., 2021).Furthermore, the interaction effect of genotype and environment on quantitative traits like seed yield means that genotypes do not yield uniformly across different areas.
In other words, genotype, environment, and genotype-environment interactions all influence each genotype's yield (Siddquie & Hoque, 2023).Understanding genotype-environment interaction effects in breeding programs can assist breeders in identifying yield variations unexplained by individual genotypes and environmental factors (Rani et al., 2021).The presence of stability in a genotype across diverse conditions indicates less genotype-environment interaction.
Therefore, modeling genotype-environment interactions in multienvironmental trials (METs) is crucial for identifying genotypes with general and specific adaptability (Kirankumar et al., 2023).
Statistical analysis methods, such as variance analysis, regression, and instability methods, have been introduced to estimate the main effects of genotype, environment, genotype-environment interactions, and stability determination (Eberhart & Russell, 1966).In most of these methods, however, some basic assumptions of stability analysis are not reliable, including the nonlinear interaction of genotype and environment, and the dependence of the independent variable (environment index) on the function variable (genotype index) (Khan, Kamran Khan, et al., 2021;Khan, Rafii, et al., 2021;Oladosu et al., 2017).In fact, it is feasible to estimate the magnitude and interaction effect of genotype-environment using multivariate methods, which include principal component analysis, additive, and multiplicative effect analysis (Bhartiya et al., 2017;Khan, Kamran Khan, et al., 2021;Khan, Rafii, et al., 2021).Additive main effects and multiplicative interaction (AMMI) analysis is a widely used multivariate stability method for investigating genotype-environment interactions (GEI).This method interprets a large portion of the GEI sum of squares by combining ANOVA for the genotype and environment main effects with principal components analysis (Gauch & Zobel, 1996;Yan et al., 2002).
Among various stability methods, the GGE biplot (genotype main effect plus genotype-environment interaction) serves as a practical graphical tool for modeling genotype-environment interaction in multi-environment trials (METs) across different crops.The GGE biplot method is capable of identifying the best-performing genotype in a given environment and the most suitable environment for a specific genotype.Furthermore, this tool assists breeders in determining the relationships between environments and in comparing genotypes based on average yield and stability (Ansarifard et al., 2020;Olanrewaju et al., 2021;Scavo et al., 2023).The use of this method has been widespread in various soybean regions, such as southern Ontario (Yan & Rajcan, 2002), India (Bhartiya et al., 2017;Samyuktha et al., 2020), northwestern Ethiopia (Atnaf et al., 2013), and South Africa (Mwiinga et al., 2020).These regions have employed the method to investigate the grain yield stability of diverse soybean cultivars across different environmental conditions, aiming to introduce appropriate cultivars for various habitats.Given the increasing need for stable soybean cultivars with optimal performance, soybean breeders are encouraged to focus on developing high-yielding cultivars that also exhibit high stability.
Evaluating genotypes using sets of traits enhances the probability of identifying the ideal genotype.The Selection Index of Ideal Genotype (SIIG) is a multivariate statistical method that identifies the ideal genotype based on a sum of traits or various indices (Zali et al., 2023).It is noteworthy that as the number of traits or indicators increases, selecting the right genotype can become challenging.
However, with the help of the SIIG discriminator, all parameters, despite having different measurement units, are consolidated into one parameter, simplifying the ranking and determination of the superior genotype (Najafi Mirak et al., 2018).This approach has been applied to a few crops, including bread wheat (Yaghutipoor et al., 2017), durum wheat (Najafi Mirak et al., 2018;Ramzi et al., 2018), lentil (Amiri et al., 2021), rapeseed (Abdollahi Hesar et al., 2021), sugar beet (Taleghani et al., 2022), and barley (Zali et al., 2023), for the assessment of superior genotypes according to a set of attributes or scales.
However, the SIIG method has not yet been utilized in soybean breeding for selecting genotypes based on different traits.Therefore, the aims of this research were to (1) investigate genotype (G), environment (E), and genotype-environment (GE) interactions on the seed yield of soybean pure lines; (2) identify the most stable lines in terms of yield and stability; (3) study the relationship among environments; and (4) select superior soybean line(s) based on the SIIG index.

| Plant material and field
Thirteen new soybean lines, along with control genotypes (Saba and Amir), were evaluated using a randomized complete block design with three replications across four locations: Karaj, Mazandaran, Golestan, and Moghan, during two growing seasons (2020-2021 and 2021-2022).Additional details about the locations and soybean lines studied are provided in Tables 1 and 2. Each experimental plot consisted of four rows, each 5 meters in length, with a spacing of 50 cm between rows and 6 cm between plants within a row.All agronomic operations, including thinning, weed, pest, and disease control, were carried out during the growth period of the soybean plants according to the cultivation instructions specific to each zone.
Phenological parameters such as days to flowering and days to maturity were recorded during the growth period of the soybeans.At maturity, five plants were selected from each plot for the measurement of agronomic properties, including plant height, node number per plant, number of pods per branch, total pod number, plant weight, number of seeds per plant, seed weight per plant, and seed yield.

| Statistical analysis
The combined analysis of variance was conducted to determine the effects of genotype, environment, and genotype-environment (G × E) interaction, assuming "year" and "location" were random factors in all environments, using SAS version 9.4 (Vargas et al., 2013).
To evaluate the stability of the seed yield of soybean lines, various univariate statistics were employed, including the coefficient of determination (R2), regression coefficient, and variance deviation from regression (Eberhart & Russell, 1966), along with stability variance (Shukla, 1972), Wricke's ecovalence (Wricke, 1962), and the stability coefficient (Lin & Binns, 1988), analyzed by R-META (Pour-Aboughadareh et al., 2019).For a better assessment of the interaction effect of genotype-environment and determination of the ideal genotype, both AMMI and GGE biplot methods were utilized using Genstat (version 12) to graphically represent the stable soybean lines (Yan et al., 2000).Finally, the principal component analysis (PCA) and the selection index of ideal genotype (SIIG) methods were applied using STATGRAPHICS (version 18) (Adilova et al., 2020) and Excel (Mau et al., 2019) to select the superior soybean line.

| Analysis of variance and mean comparison of each trait
The combined analysis of variance (ANOVA) showed that all studied traits were significantly affected by the main effects of genotype, environment, and genotype-environment (G × E) interaction (Table 3).Table 4 revealed that the average plant height was 88.42 cm, with the highest and lowest heights being 115.1 cm for line 8 and 64.9 cm for line 2, respectively.The node number ranged between 12.8 (line 2) and 18.6 (line 1), averaging 15.62.The maximum and minimum branch numbers were observed in soybean lines 8 (3.5) and 3 (1.9), with an overall average of 2.72.The average number of total pods was 65.94, ranging from 50.2 (line 10) to 80.4 (line 2).The heaviest and lightest plant weights were recorded for line 12 (87.7)and line 10 (48.7), respectively.The highest seed yields belonged to line 2 (3348.7 kg ha −1 ) and line 5 (3142.8kg ha −1 ).The earliest maturing lines were lines 1 and 5, both reaching maturity in 128 days.Taking into account seed performance and maturity, line 5 was ranked as the top-performing line among the others (Table 4).

| Additive main effects and multiplicative interaction (AMMI) analysis for grain yield
The AMMI analysis for seed yield demonstrated a highly significant effect of environment, genotype, and genotype-environment interaction.The effects were rated as E > GEI > G, contributing 65.89%, 29.58%, and 4.5%, respectively (Table 5).The AMMI model, based on partitioning the GEI, indicated that the first five terms of AMMI were significant, explaining 96.35% of the GEI variance.
Specifically, the first and second principal component axes (IPCA) of the interaction explained 48.70% and 24.97% of the GEI sum of squares, respectively (Table 5).Among the eight testing environments, seed yields were highest in Moghan in the first year, with TA B L E 1 Agro-climatic characteristics of the environments studied in this research.an average of 4118 kg ha −1 , followed by Moghan in the second year with 3892 kg ha −1 (Table 6).Conversely, the lowest seed yields were recorded in Mazandaran in the second year (2342 kg ha −1 ) and the first year (2346 kg ha −1 ).The mean grain yield of genotypes across environments (Table 6) showed that line 2 (3348.7 kg ha −1 ) and line 5 (3142 kg ha −1 ) were the highest yielding genotypes, while genotype line 12 yielded the lowest at 2590.4 kg ha −1 .

| Evaluation of various parametric stability
The yield stability criteria were evaluated using various parametric methods (Table 7).The data indicated that the mean square of each line was significant for seed yield.According to the regression coefficient, lines 5, 8, 10, 12, and 14 were more sensitive to environmental changes and had specific adaptability to high-efficiency environments, as indicated by their regression coefficients being greater than 1.Conversely, lines 1, 2, 3, and 6 exhibited the highest tolerance to environmental changes and adaptability to lowefficiency environments due to regression coefficients less than 1.
According to Wricke's ecovalence stability parameter, lines 2, 10, 13, and 14 had the lowest coefficients, marking them as the most stable lines, while lines 8, 4, 7, and 6, with the highest ecovalence, were considered the least stable.
The mean deviation from regression is another stability factor, with genotypes closer to zero or having minimal deviation being more stable.Therefore, lines 2, 10, 13, and 14 were the most stable, having the least deviation from regression.Lines 1, 4, 7, and 8 exhibited the highest deviation from regression, indicating lower stability.The coefficient of determination (R2) data showed that lines 4 and 6, with the lowest R2, were more stable.The coefficient of variation (CV) results indicated that genotypes with lower CV, such as lines 2 and 6, had higher stability.According to the Lin and Binns indicator, lower values of this parameter signify greater stability.Hence, lines 2, 5, 6, and 14 were selected as the most stable lines.Furthermore, the BLUP stability measurement, an effective approach for multi-environmental analysis, was used to estimate genotype means with high accuracy, reducing G × E interaction, and selecting high-yield genotypes based on a combination of stability and performance.Based on this parameter, lines 2, 5, and 8 were identified as the most stable lines (Table 7).

| Polygon view of GGE biplot to group lines and environment
In the polygon view, the soybean lines positioned at each vertex of a sector indicated the best-performing lines in the test environment TA B L E 3 Combined analysis of variance different traits of 15 soybean lines across 8 environments (combination of years and locations).(Figure 1).The last ME contained Karaj 1, where soybean line 7 yielded 2822 kg ha −1 .Soybean line 12 was not considered superior and showed the least yield in all MEs.Furthermore, lines 5, 10, 13, and 14, with yields of 3142, 2959, 2787, and 2980 kg ha −1 , respectively, exhibited the least genotype-environment (GE) interaction, emphasizing their suitable general adaptability to all environments (Figure 1).

| GGE biplot analysis based on comparison of all lines with ideal line
The ideal genotype should exhibit the highest average performance and stability across the tested environments.Such a genotype is represented by the longest vector length among genotypes with high average performance, coupled with a minimal contribution to genotype-environment (GE) interaction.Although an ideal genotype in this precise form may not exist in practice, it serves as a benchmark for genotype evaluation.The proximity of a genotype to this reference indicates its ideality.For the assessment of the ideal genotype, GGE biplots use concentric circles to graphically determine the distance between the studied genotype and the ideal genotype (Figure 2).Consequently, soybean lines 6, 2, 7, and 5, with yields of 2992, 3348, 2822, and 3142 kg ha −1 , respectively, were selected as ideal genotypes due to their proximity to the ideal genotype and their high yield and stability (Figure 2).In contrast, lines 12, 1, 15, and 4, with seed yields of 2590, 2764, 2817, and 2879 kg ha −1 , respectively, were identified as less favorable genotypes based on their greater distance from the ideal genotype (Figure 2).It is important to note that examining stability alone is not sufficient; less stable cultivars with good average performance can be preferable over stable cultivars with inadequate yields.

| Biplot view for synchronous evaluation of lines based on stability and yield
An important aspect of the GGE biplot model is the simultaneous assessment of genotypes according to yield and stability.Figure 3 displays the ranking of 15 soybean lines according to their seed yield and stability across various environments.
The genotype is positioned into nearness to the concentric rings, determining the best-performing genotype, and the projection from the average environment axes (AEA) abscissa indicates the genotype's stability.Genotypes are considered being more stable when they are placed on the horizontal axis (AEC abscissa) and have zero projection from the vertical axis (AEC ordinate), while the genotype with the longest direction from the AEC abscissa is treated as unstable; a similar report was stated by Oladosu et al. (2017).

F I G U R E 1
The polygon view of the GGE biplot to show megaenvironments and their superior lines.Refer to Tables 1 for line name.
F I G U R E 2 Biplot view to compare the studied lines with the ideal line.Refer to Tables 1 for line name.the genotype's stability.The more distance of genotypes from AEC, the less stable genotypes appear (Oladosu et al., 2017).According to the results, soybean lines 15, 11, 13, and 3 exhibited the highest stability with average yields of 2817, 2840, 2787, and 2774 kg ha −1 , respectively (Figure 3).Lines 6, 5, and 2 showed average stability with yields of 2992, 3142, and 3348 kg ha −1 , respectively.Conversely, lines 8, 1, and 4 were more unstable with performances of 2995, 2764, and 2879 kg ha −1 , respectively (Figure 3).
Additionally, these lines were grouped into clusters along the vertical line on the AEC.The first group (upper) and the second group (lower) contained lines with higher and lower average yields than the median yield.Consequently, lines 6 and 5 were identified as the most stable lines with yields of 2992 and 3142 kg ha −1 , respectively (Figure 3).

| Selection index of ideal genotype (SIIG)
In this study, the selection index of ideal genotype (SIIG) was calculated based on 11 traits, excluding seed yield, to select the best genotypes.The ideal genotype was defined as the one with higher values in traits such as plant height, node number per plant, number of branches per plant, number of pods per branch, total pod number, plant weight, number of seeds per plant, and seed weight per plant, and lower values in days to flowering, days to pod formation, and days to maturity.By utilizing the SIIG index, these attributes are consolidated into a single index, enabling more reliable and accurate selection of superior genotypes.The SIIG index ranges between 0 and 1.A genotype with an SIIG close to 1 indicates a more favorable condition in terms of most investigated traits, while a lower SIIG suggests less desirable conditions.According to the data, soybean lines 8, 1, and 5 emerged as superior with the highest SIIG values of 0.687, 0.651, and 0.634, respectively (Table 8).Conversely, lines 10, 3, and 15 had the lowest SIIG values of 0.215, 0.387, and 0.405, respectively.
Additionally, a two-dimensional graph was used for the simultaneous selection of lines based on agronomic traits and seed yield.
Figure 4 showed that soybean lines 1, 5, and 8 were superior, having higher SIIG and seed yield.However, lines 3 and 15 were identified as the least desirable lines in terms of the traits studied.
F I G U R E 3 Biplot view for simultaneous selection of seed yield and stability of the studied lines.Refer to Tables 1 for lines name.

TA B L E 8
The SIIG of soybean lines according to all traits studied following distance from desirable line (d + ), none desirable line (d − ), and seed yield.
The two-dimensional of distribution of 15 soybean lines based on seed yield and SIIG.

| Principal component analysis (PCA)
The results indicated that the first three components, each with values higher than 1, accounted for 81.22% of the total variance of variables (Table 9).In the first principal component (PC1), the phenological traits included days to flowering (DAF), days to pod formation (DAPF), and days to maturity (DAM) with coefficients of 0.46, 0.47, and 0.46, respectively.In PC2, the highest coefficients were associated with the total number of pods (0.47), seed weight per plant (0.49), and the number of seeds per plant (0.54).Finally, for PC3, the parameters of plant weight, node number, and plant height showed the highest positive coefficients at 0.45, 0.49, and 0.57, respectively, while seed yield had the highest negative coefficient (−0.44).the highest positive projections for the seed yield parameter, could be selected as high-yield lines (Figure 5).Additionally, lines 12 and 8, with the highest projections but in the opposite direction to seed yield, are indicated as lines with low yield.Line 5 was also selected for its high yield and earliness (Figure 5).

| DISCUSS ION
A significant portion of Iran's annual income is allocated to importing oilseeds like soybeans for essential oils and proteins needed in human and livestock diets.Consequently, increasing soybean cultivation area and yield is crucial for reducing reliance on imports.
Soybean in Iran has adapted to various environmental conditions, making the development of genotypes with high adaptability to diverse environments a key goal in plant breeding.
The performance stability of a variety refers to its consistent production in a specific environment over time (Mirza et al., 2013).A plant variety's ability to tolerate different stresses (such as temperature extremes, water levels, day length changes, and light intensity)  survive a range of soil conditions is essential for growth and development (Kumaresan & Nadarajan, 2010).Genotype and environment interaction (G × E interaction) occurs when plant genotypes respond differently to environmental changes, impacting the relationship between phenotypic and genotypic values.This interaction reduces the effectiveness of the selection process in plant breeding, which relies heavily on accurate phenotypic predictions (Dia et al., 2016).Addressing this requires selecting stable genotypes with minimal G × E interaction and developing genotypes with lower G × E interaction effects by dividing heterogeneous environments into more homogeneous ones (Farshadfar et al., 2011).
In the present study, the stability of 15 soybean lines under various Iranian environmental conditions were evaluated.Combined ANOVA analysis revealed that genotype, environment, year, and their interactions significantly influenced all traits studied.The  Centeno and ICNBF 8-611, as highly stable, while others such as Gloria and Ehbytm80-1 were noted as low stable genotypes (Bahrami et al., 2009).Our findings highlighted that soybean lines 2 and 5, with yields of 3349 and 3143 kg ha −1 , respectively, were selected as the more stable lines among others.This was based on stability factors such as lower values of Wi 2 , σ 2i , P i , and s 2 di, a high BLUP factor, and bi equal to 1.The use of different parametric stability assessments has also been reported in wheat (Bornhofen et al., 2017), rice (Lee et al., 2023), safflower (Afzal et al., 2021), and oat (Kebede et al., 2023).
Based on multivariate analytical methods, the AMMI and GGE biplot are valuable tools for identifying stable lines in various environments.These tools consider different characteristics related to the performance of the tested lines (Zhang et al., 2016).Ruswandi et al. (2021) have highlighted the effectiveness of the GGE biplot in graphically displaying the relationships between genotype, environment, and G × E interactions.The GGE biplot's polygon view, known as "which won where", is a critical graphical pattern for recognizing mega environments and determining the best genotype for each.
This approach has been applied in numerous studies across different plant species, including groundnuts.In the current study, the polygon plot of the GGE biplot revealed five mega environments, each with specific superior lines identified as vertex lines (1,2,4,6,7,8,12).
These lines performed better or worse in some or all environments due to their distance from the biplot's origin.Conversely, soybean lines 5, 10, 13, and 14 were near the biplot origin, indicating average The GGE biplot has the unique capability of identifying the highest yielding genotypes across different environments, referred to as the "ideal genotype".This tool is particularly effective due to its ability to predict both the average yield of a genotype and its stability and adaptability to specific environments, as outlined by Santos et al. (2017).In our study, soybean lines 2, 5, 6, and 7 were identified as desirable due to their proximity to the ideal genotype.This finding aligns with the work of Ansarifard et al. (2020) and Stansluos et al. (2023), who employed the GGE biplot for evaluating and selecting outstanding genotypes based on various agronomic traits.While the outcomes of parametric stability analysis methods largely concurred with the GGE biplot analysis, additional stability approaches were necessary to categorize stable lines and reinforce our results.The findings of our study are in agreement with previous research conducted by Mohammadi and Amri (2008) and Ruswandi et al. (2022).
Another tool for ranking and comparing various genotypes is the SIIG index, which is superior to other methods.The SIIG method can select the appropriate genotypes based on different traits, such as morphological and physiological characteristics.Indeed, this method can sum all traits and indexes into one index to more easily rank the best genotype (Mirzaei & Hemayati, 2021;Zali et al., 2023).According to the SIIG index in the present study, the soybean lines 8, 1, and 5 were chosen as superior lines based on the maximum amount of agronomic traits and the minimum of phenologic parameters.Zali et al. (2023) reported on the identification of superior barley genotypes using the SIIG method, which led to the introduction of genotypes 4, 8, 31, and 28 as the ideal genotypes for different tested environments.In another study, Gholizadeh et al. (2021) expressed that the SIIG index was an applicable method for effectively screening ideal genotypes in sunflowers by combining various agronomic traits.
To classify soybean lines, a multivariate method called principal component analysis (PCA) was used, which showed that the total variation exhibited by PC1, PC2, and PC3 were 32.87%, 26.81%, and 21.54%, respectively.PC1 was positively associated with phenological traits.PC2 was connected to yield components such as TP, NS/P, and SW/P.It was evident that the high coefficient of the expressed traits was due to the increment of TP and NP/B, which caused the increase of NS/P, SW/P, followed by yield (Y). PC1 was positively related to PH, NN/P, and SW/P, as well as negatively linked to Y.This issue corresponding to that particular sector, identified by the greatest distance from the center.According to the vertical lines of the polygon side, there were five mega-environments (MEs) encompassing six soybean lines (Figure1).The first ME included two out of eight sectors (Golestan 1 and 2) with line 4 being superior and showing the highest yield of 2879 kg ha −1 .The second ME comprised Moghan 2, where soybean line 15 had the highest yield of 2817 kg ha −1 .The third ME consisted of two sectors, Mazandaran 1 and 2, with superior soybean lines 2, 8, and 1 yielding 3348, 2995, and 2764 kg ha −1 , respectively.The fourth ME included Karaj 2 and Moghan 1, with soybean line 6 yielding 2992 kg ha −1 The line marked with an arrow, representing the average coefficients of the first two components of the GGE biplot model, passes from the center of the biplot to the desired point and is known as the average environment coordinate (AEC).Genotypes closer to the concentric rings demonstrate the best-performing genotypes and the projection from average environment axes (AEA) abscissa indicates TA B L E 7 The parametric stability criteria in the studied soybean lines.

Figure 5
Figure 5 displays the location of each trait and genotype on a plot generated using PC1, PC2, and PC3.The graphs for traits that are related to each other align in the same direction, whereas those with inverse relationships do not align.This figure enables the selection of different lines based on various traits.A line is drawn from the related trait to the origin of the coordinate system, followed by another line passing through the origin, which is vertical to the first line.Lines with the highest projection on the first line and located on the side of the concerned trait relative to the vertical line have the maximum value of that trait.Conversely, the minimum values of the traits are determined by the direction opposite to the concerned traits relative to the vertical line.For instance, lines 2 and 5, with

F
The three significant components plot obtained by principal component analysis in order to locate traits and lines.Y: yield; NN/P: number of nodes per plant; PH: plant height; PW: plant weight; R1: days to flowering (DAF); R2: days to pod formation (DAPF); R3: days to maturity (DAM); NB/P: number of branches per plant; NP/B: number of pods per plant; SW/P: seed weight per plant; NS/P: number of seeds per plant; TP: total pods per plant.
environment contributed 65.89% to yield variability, more than genotypes (4.5%) and G × E interaction (29.58%), indicating considerable environmental variability across different climatic conditions.This finding aligns with reports by Liu et al. (2017), Hailemariam Habtegebriel (2022), and Susanto et al. (2023), underscoring the significant influence of G × E interaction on soybean yield, which reflects the varied responses of genotypes to different environments.When the presence of GEIs was confirmed through combined ANOVA analysis and the AMMI model, various stability measurements were used to evaluate the stability and compatibility of genotypes across different environments.Researchers have employed several methods for multi-environmental examination to accurately select stable and high-yielding lines, as referenced by Ahmadi et al. (2015), Vaezi et al. (2019), and Maulana et al. (2020).
performance and lower GEI variation compared to the vertex genotypes.This pattern aligns with findings from Adham et al. (2022), Bilate Daemo et al. (2023), Esan et al. (2023), and Kindie et al. (2022), who reported on dividing testing environments into various mega environments with different sectors and numbers of genotypes.
The name and pedigree of each soybean line.
Abbreviations: m.a.s.l, meter above sea level; mm, millimeter; the average temperature is for two years of experiment.TA B L E 2